Algorithmic Templates and Multiset Problems in Graphs
The results in this dissertation comprise a contribution to the developing theory of linear/polynomial algorithms for graph theoretical problems. Further, a new class of graph theoretic problems is defined, and both theoretical and computational considerations are discussed.
Much algorithmic work has been done (and is currently being done) on the classes of partial k-trees, and here the focus is on partial 2-tress, better known as series-parallel graphs. An algorithmic template, which isone algorithm that can be used to solve several different parameters on a specified class of graphs, is introduced for the class of series-parallel graphs.
The new class of problems defined here is the class of multiset/single property problems. In addition to practical applications associated with specific problems in this class, the problem type per se has theoretical computational interest.
Both the study of templates and the study of multiset problems are intended to increase our understanding of the nature of the problems for which linear/polynomial algorithms can be developed for appropriate classes of graphs.